Question

Ajutati-ma va roog.
a) $5^{1+2+3+3+...+2014} = 5^{n+1007}$

b) $7^{2+4+6+...+100} = 7^{n(n+1)}$

30 PUNCTE :)

Answer 1

a)1+2+3+...+2014=2014*2015/2=1007*2015⇒1007*2015=n+1007⇒
n =1007*2015-1007⇒n= 1007(2015-1)⇒n=1007*2014
b) 2+4+6+...+100=2(1+2+3+...+50) = 2*50*(50+1)/2=50(50+1)⇒n(n+1) = 50(50+1)⇒n=50

Answer 2

$a) 5^{1+2+3+...+2014}= 5^{ \frac{2014*2015}{2} }= 5^{4058210} \\ n= 5^{4058201}: 5^{1007}=4057203$